Structure and ionic conductivity of mixed lead halides PbCl2xBr2(1−x). II

Solid State Ionics 20 (1986) 295-304 North-Holland, Amsterdam

STRUCTURE AND IONIC CONDUCTIVITY OF MIXED LEAD HALIDES PbCl2x Br2( 1 -x)" II. M. LUMBRERAS C.L.O.E.S., Laboratoire de G~nie Physique, Universit~ de Metz, 5704.~ Metz Cedex 1, France

J. PROTAS, S. JEBBARI Laborato~re de Cristallographie, Universit~ de Nancy L P.O. Box 239, 54506 Vandoeuvre-les-Nancy, France

G.J. DIRKSEN Solid State Department, Utrecht University, P.O. Box 80000, 3508 TA Utrecht, The Netherlands and

J. SCHOONMAN Laboratory of Inorganic and Physical Chemistry, Delft University of Technology, P.O. Box 5045, 2600 GA Delft, The Netherlands

Received 23 December 1985; accepted for publication 5 Februaxy 1986

PbCI^ and PbBr 2 show complete mutual solid solubility. The solid solutions PbCl2xBr2:1 x~ exhibit the PbCl2-type orthorhombic symmetry. XRD measu~emeflts show preferential site occupancy. The ionic c o n d u c t i v i t y has been measured as a function of temperature and composition. The ionic conductivity of PbCIBr in which the anion array is completely ordered, is slightly anisotropic. Homovalent anion doping causes the c o n d u c t i v i t y to decrease. The role of preferential site occupancy, and dopant induced lattice distortions on the number and mobility of the conducting defects is discussed.

over different

i. INTRODUCTION

Complete Phase

relationships

PbCI2-PbBr 2 time

ago

have (I,2).

relationships BaBr 2 (4)

(3), have

literature. PbCl2-type

in and been All

in

been

the

system

reported

More

recently,

the

systems

some phase BaCl 2-

PbX2-PbI 2 (X = CI,Br) described the

systems

orthorhombic

in

the

exhibit

symmetry,

but

0 167-2738/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

in

composition

mutual

the systems

PbBr 2,

due

solid solubility

to

show anion

anions.

All

binary

anion

end

conductivity

mechanism,

and

compositions

ordering

the size disparity

different the

exists

BaCl2-BaBr 2, and PbCI 2-

In all the systems,

occur which

ranges.

between

members via

recently

effects

a it

the

exhibit vacancy has been

M. Lurnbreras et al./Mixed lead halides PbCl2xBr2( 1 -x). H

296

shown

by

the

preferential

present

site

ordering

effects

electrical in

the

(5).Homovalent substantial several Frenkel

type halides

It

the

that

occur.

The

In

this

the

paper

solutions

solutions

in

is

the

and

relation

for

system

the the

the

PbC12-PbBr 2

properties

analyzed squares

solid

homovalent

anion

be

regarding

electrical

to and

to

electrode

By

EXPERIMENTAL

Single

of

(0 • x • i) w e r e technique

zone-refined Microprobe

(5).

The

a

CAD

XRD m e a s u r e m e n t s 4

ENRAF-NONIUS

diffractometer radiation After

Stuart

using

for

method

(15),

PbCl2-type the

PbBr 2.

In this

occupy

the

linear

were least

procedure

(9).

dimensions

equivalent

the

circuit checked.

short

are

two

accommodate

taken

site

1 (Figure

by W a l k e r

the

The v a r i a t i o n and

PbCI 2the atoms

special positions g r o u p D 216 h - P n a m : they perpendicular

at z = + 1/4.

non-equivalent

PbCl2-type

AgK~

all

plane,

can

or

system

c-axis

the

on

entire structure

of the s p a c e

the

is o b s e r v e d

fourfold

the

to

following

Lorentz

as an

spectra

structure

mixtures

monochromator.

proposed

and

(5). actual

automatic

CuK~

graphite

absorption,

empirical

the

were

a

3. R E S U L T S

PbBr 2

close

used

was

lie on a m i r r o r

the s t a r t i n g

non

sample of

4(E)

be

of

nature

and

Response

dag was

fitting

the

Bridgeman

and

(GRI680A),

a

computer

impedance automatic

material.

using

throughout

revealed

by an

admittance

materials

to

compositions

contact and

dependence

of the s o l i d

Frequency

Graphite

by the

PbCI 2

studied

bridge

as s t a r t i n g

analysis

compositions

conductivity

anion

distribution.

PbCl2xBr2(l_x)

grown

using

I. The

in

ASPECTS

crystals

ratio.

in T a b l e

parameters

The 2.

vibration

using

varying

bulk

thermal

gathered

I172

Impedance

distortions.

information

structural

defect

densities

complete

occupancy

were

Analyser.

influence

the

and c o m p o s i t i o n

ionic

Solartron

assumed

lattice

the

the

refined procedure

site

spectroscopy

solid

of

we p r e s e n t

quantitative

doping,

on

based

and

are

of

defect

mobility by

Details

were

giving

anisotropic

parameters,

temperature

distortions

larger

unaffected

matrix,

or

these

enthalpy

that

program)

capacitance

in

lattice

(Shelx

data

least-squares

Schottky

respectively,

all

a

in

solutions

(6),

corrections, using

increases

conducting

formation

such

induces

(7,8).

assumed

solutions

doping

solid

halides

is

solid

PbC12-PbBr 2

conductivity

alkali

the

of

system

ion

cation

that

and a n i o n

decrease

conductivity

solutions

silver

authors

occupancy

structure. larger

sites

Anion

ions

than

of the

lattice

volume

site

2

anion

parameter

presented

in F i g u r e

Numerical

values

parameters

versus x is

2.

and

polarization

in

i).

cell

compositional

anion

to

There

are g a t h e r e d

in

the

M. Lurnbreras et al./Mixed lead halides PbCl2xBr2( 1-x). H

297

TABLE 1 XRD MEASUREMENTSAND ANALYSIS x = 1

x = 0.76

x = 0.54

x = 0.30

x = 0

(PbCI 2)

(PbBr2)

i

[0,30]

[0,30]

[0,30]

[0,30]

[0,30]

H min, H max

0;13

0;13

0;13

0;14

0;16

K min, K max

0;16

0;16

0;16

0;16

0;19

L min, L max

0;8

0;8

O;B

0;8

0;9

number of independant reflections

1213

1234

1304

1308

1692

449

376

364

308

645

21

20

22

22

21

2.68

3.65

1.56

2.78

2.49

R index

0.0323

0.0417

0.0262

0.0365

0.0314

Rw index

0.0324

0.0418

0.0263

0.0342

0.0316

Theta range (with AgK~ radiation)

number of reflections with I > 3 ~ I ) number of refined parameters statistical

factor

1/ 2 for all solid solutions

weighting scheme maximum electron density in final difference Fouler synthesis take-off angle

~ ~1411~.

=

1.79

3.78

2.18

2.31

40

40

30

405

Table

b

3#*

If.

The

site occupancy thermal

for

Figure

I.

"31~ c-axis

PbCI 2 structure.

)31/~

projection

of

the

fractional

isotropic

selected

presented

t g3~

50

coordinates,

several

OC[ 1 ec[ 2

1.71e~ -~

in

the w e i g h t i n g

Here w stands

factor

and u for the

variations

of the shortest wi~h

The

usually

reveal

semicircles, intercept

displacement.

composition

3.

are

III.

thermal

Figure

and for

solutions

isotroplc

distances

factor,

parameters

solid

Table

atomic

are given

admittance two strongly the

representing

The

interatomic in

spectra depressed

high-frequency the bulk

ionic

11,[. Lumbreras et aL/Mixed lead halides PbCl2xBr2( 1-x). H

298

~ 3 [ ~ ~ - ~

d(~k)

d(,~)

a

b

350

-

310~

,,~9.5

8.0

.I

7.81 ~

, z.s~

2.5

--

~.S I

I

d(A) 4

I

1 0.8 0.6 0./~ 0.2 0 (pbE[2) x (PbBr21

diAl

c

1 ,d

3.5 Figure

2:

Lattice p a r a m e t e r s and cell volumes of P b C l 2 x B r 2 ( l _ x ) crystals.

3.. =

3

3 I

conductivity. solutions

The could

equivalent parallel combination

spectra be

circuit (P)

fitted

solid to

comprising

branches of

of all

a resistance

(R)

Figure

x 3:

an two (S)

a.

Pb-Cl

and a

b.

Pb-CI 2

of a series

°

0

I

x

V a r i a t i o n of the shortest interatomic distances with composition.

I

c.

CII-CI 1

d. C12-CI 2

TABLE II LATTICE PARAMETERSAND CELL VOLUME VERSUSTHE MEASUREDCOMPOSITION. x (%)

a (o) ~

b (o) ~

c (o) ~

V (o) ~3

ioo 84.4 76.o 55.4 53.6 44.4

7.619 (3) 7.678 (2) 7.711 (I) 7.783 (I) 7.801 (2) 7.8291(8)

9.043 (2) 9.085 (2) 9.119 (3) 9.1825(8) 9.200 (I) 9.2383(7)

4.5336 4.5505 4.5609 4.5725 4.5790 4.5982

3o.1 16.7 o

7.9o71(7) 7.9666(6) 8.o59o(2)

9.3350(8) 9.413o(6) 9.540 ( i )

4.6513 (2) 4.6869 (5) 4.7319 (4)

(6) (8) (7) (9) (7) (4)

312.33 317.4o 320.70 326.80 328,64 332.58

(20) (21) (18) (14) (15) (9)

343.33 (7) 351.47 (9) 363.79 (15)

0

M. Lumbreras et aL/Mixed lead halides PbCl2xBr2( 1 -x). II

!

!

I

PbCIo.IBrl.9 607K

~3 x

2

o2

E u) v I-. b

1 0 Figure

2

I 4:

3 4. _- 104"x y' (S)

Admittance

frequency

1.6

x 10 - 2

10 5

Hz

I

|

I

I

I

I

300

250

200

150

1

T °

5

-1

recorded

the

I

a

of

spectrum

PbClo.iBrl.9

299

in

range

-2

to

at 6 0 7

K. -3

constant

phase

angle

impedance

ZQ = k(iw) -~

element

Q with

(0 • ~ • i).

The 10 5

equivalent

circuit

by R Q S R Q S P .

A representative

spectrum The

is g i v e n

can be r e p r e s e n t e d

in F i g u r e

temperature

dependence

of the

PbCl2xBr2(l_x~

presented

in F i g u r e

The

composition

formation enthalpy The

Figure

5:

in F i g u r e

analysis that

The

and

is

is

the

1

I,b

T O

6.

based

on

the

disorder

conductivity

PbCI2xBr2(I,x)

crystals

measured

the

along

I

÷

migration

Schottky

ionic

of

i

of E

dependence

is g i v e n

assumption

crystals

,

b

composition

5.

enthalpy

data

!

conductivity

several

(

admittance 4.

and ionic

(K-l)

of

-1

-2

-3

b-axis. A. x = 0(I),

x = 0.3(2),

x = 0.5(3) B.

x

=

0.75(I),

x = 0.64(3),

x

=

0.95(2),

x = 0.5(4).

I

i

I

300

250

200 lOJ (K -1 ) ( T

I 150

300

M. Lurnbreras et al./Mixed lead halides PbCl2xBr2( 1 -x). H

DISCUSSION

PbCt2xBr2(1-x)

All

!

two

[

PbCI 2

anion

occurs.

Ii

completely anion 0

I

I

x

Br

E

The in

sites

1 remain

ions,

I

I

075

05

025

reversed

by

while

by Cl

and

the

situation

solutions

the

anion

Cl-

and

2 remain

In

i

with

sites Br-

occupied

ordered

1

ions,

with

are while

Br

array

is x <

ions.

of

the

sites

1 are

0 equimolecular occupied

of the f o r m a t i o n

ions.

aHf of S c h o t t k y

defects,

and m i g r a t i o n

enthalpy

aH of a n i o n

a

composition

by

These

Cl

,

and

results

structure

accommodate

m

vacancies

occupancy

sites

by C1

solid

Here

occupied

enthalpy

discerned.

2 are o c c u p i e d

ions.

0.5.

Variation

be site

0.5

occupied

sites

observed

6:

>

the

in w h i c h

I

>

Figure

can

anion

For

adopt

structure

sites

Preferential

i I

I

solutions

solid

orthorhombic

sites

are c o n c o r d a n t

in

which

larger

anions

The

isotropic

the

cations

2 by Br

thermal

site than

with

2

can

site

i.

displacement

of

in

PbCl2xBr2(l_x)

with

thermal

and

anions

vibrations

reveal

to be n e a r l y

the equal

composition. and

weak

at

indicating prevails

in

the

the end m e m b e r s x > 0.5

V~l

species,

be

for

region

yield &Hf/3.

or

intrinsic ionic

can

Br~r

1 and Br-

(viz.

Table

<

0.5

V~r

the

analysed were

and

impedance of

to to

extrapolate values,

this

sites,

the The

conductivity.

the

circuit

Cl~r

data the

ions

reveal

equimolecular anisotropic. CI-

sites

ions 2

In

occupy

ionic

607 (RI I cell 2.51

K

R21 )

constant x

zero

10 -2

conductivity.

The

spectra

the all

conductance

support

to

the

of the e l e c t r i c a l

Fitting

to

analysis

is b e y o n d

d.c.

nature

the

equivalent

to the s m a l l - s i g n a l

spectrum

leads +

conductors

A detailed

lends

are

in a c c o r d a n c e

spectra

RIQISR2Q2SP

admittance

ionic

paper.

to

which

temperature

lead h a l i d e s

temperature

observation. the

scope

Br~l

these

defect-type

ambient

also y i e l d s A H f / 3 .

compound

III).

at

of

CI~I

to be s l i g h t l y

sites

If for

classical

with

vacancies

and

of

ordered

in

that

purely

conductivity

compound

as

to be the m o b i l e

be

over

region

conductivity

this

x

If a n i o n

distributed

sites,

solution

PbCI 2 and PbBr 2.

is a s s u m e d

and

intrinsic

solid

ambient

of P b C I 0 . 1 B r l . 9 at

numerical

which

values

together

with

for the

lead to the v a l u e S m -I for the bulk For c r y s t a l s

ionic

of the same

M. Lumbreras et aL/Mixed lead halides PbCl2xBr2( 1 -x). 1I

TABLE I l l FRACTIONAL ATOMIC COORDINATES, SITE OCCUPANCYFACTOR, AND EQUIVALENT ISOTROPIC THERMAL PARAMETERS FOR SELECTED PbCI2x Br2¢l_xl CRYSTALS. FOR ALL ATOMS AND ALL COMPOSITIONS z/C : 0.25.

x

atoms

x/A

Y/B

lliwiu i

K

ziwi

0.76

0.54

0.3

C11

0.8570 (5)

0.0734 (4)

0,95 (2)

0,123

C12

0.4776 (5)

0.8386 (5)

0.98 (3)

0.143

Pb

0.2611 (I)

0.0953 ( I )

1.00

0.150

C11 Br I

0.8583 (7)

0.0704 (6)

1.00 (0) 0.00 (0)

0.127

C12 Br 2

0.4724 (4)

0.8322 (4)

0.54 (I) 0.47 ( i )

0.131

Pb

0.2543 (2)

0.0993 (I)

1.00

0.161

Cll Dr I

0.8576 (4)

n.0685 (3)

1.01 (0) 0.01 (0)

0.143

C12 Br 2

0.4714 (2)

0.8315 (I)

0.04 (3) 0.96 (3)

0.143

Pb

0.2468 (2)

0.1035 ( i )

1.00 ( i )

0.173

Cll BrI

0.8572 (4)

0.0733 (3)

0.55 (3) 0.45 (3)

0.135

C12 Br2

0.4752 (3)

0.8337 (2)

0.06 (4) 0.95 (4)

0.149

Pb

0.2556 (3)

0.0966 (1)

1.00

0.178

Br I

0.8576 (2)

0.0778 (1)

0.991 (1)

0.141

Br 2

0.4807 (2)

0.8376 (2)

1.01

Pb

0.2657 (i)

0.0884 (i)

1.00

(i)

,0.157

0.173

301

.4/[. Lumbreras et al./Mixed lead halides PbCl2xBr2( 1 -x). 1I

302

PbBr 2 I

I

I

~ PbCIBr

conducting solid

Schottky

solutions

anion

%,

Similar the

b

the

Br2(l_x~.

proposed

-3

halides I 200

I 150

and

105 I) < Z (KFigure

7:

Temperature

dependence

ionic

conductivity

along

the a - a x i s ( l )

of

the

of P b C I B r and

b-axis(2).

composition

and

dimensions

large-signal

independent yield the

conductance

the

value

bulk

data

ionic

2.49

(i0).

the

will

ionic region

increasing

solute around

composition conductivity

be

Conductivity

extrinsic

occurs

data

sample

local

the

PbCiBr. decreases

hindrance due

to

dopant

enthalpy

for

(8,12). present

with

A minimum

intrinsic

in the s e q u e n c e

anion

The

vacancy

in s e v e r a l to a

interstitial

ion

larger ion.

size

of the

The m i g r a t i o n

as

while

less

invariant,

around

the

the

enthalpy

increasing

from

or

on dopant

solutions

the

the

affected migration

depending

isotherms

Apart

ions

though

migration

content, conductivity

met

solid

with

positions

< 1 holds.

solute

smaller,

increases

minimum.

the

vacancy

are

In

V' Ag Ag i are

ions

is m u c h

Usually

ion size

in the

silver

is a s c r i b e d

seems

mobility

the

defect

In

interstitial

It

reported isotherms

of the

homovalent

slightly

equimolecular The

steric

enthalpies

that

and m e m b e r s

is

which

motion

an

ion v a c a n c i e s

silver

situation

exert

on the d e f e c t

such

pure

solutions,

increases.

it has strain

effect

py:g/PAg~.~

~ull

decrease

content.

reversed

(8).

conductivity to

ratio

PbCl2x

elastic

enhanced.

the

to

anion

halides

ions will

silver

mobility

(GRI680A)

The

both

In

vacancy

for

are

mobile.

frequency

x 10 -2 S m -I

conductivity.

analysis

elsewhere reveal

varying

larger

interstitial

solid

that

enthalpy

densities

for

solutions

(7,8)

by

formation

to be of more

observations solid

in

though,

in c o n t r a s t

For the s i l v e r

appreciable

observed

(1_!1)

the p h e n o m e n o n

introduced -2

have been

applicability,

present

been

substantial e.g.

KCI-RbCI

conducting

-I

by h o m o v a l e n t

exhibit

and A g × x I l _ x (7,8).

system

general

i°

obtained

effects

indicating

o

Frenkel-type

enhancements,

KClxBrl_x(6),

I 250

cation

or

doping

conductivity

I 300

~ PbCI 2. U s u a l l y

I

solute extrinsic

reveal several

a com-

equimolecular

M. Lurabreras et aL/Mixed lead halides PbCl2xBr2( 1-x). H

composition

PbCIBr,

formation

question,

decreases

with

solute

content.

The

therefore,

arises

enhanced

modified taken

into

reveal

in

the

roughly

the

need

The a n i o n

undoped

. ~VBr

up t o

to

to be

room

~V~l 630 K (11,

122).

~ (PbBr 2)

>

~

(PbCI2)

(PbCI2).

with

This

densities

implies

in

roughly

in

isotherm,

With

we must to

solutions,

effects

regard

occur

in

within

indicating

(i - ~ ) rBr by lowering

are

to

reduced

densities.

are

magnitude,

10

the

conductivity defect

the

slightly

solid

enhanced

However,

one that

all

order strsin

of of a

magnitude exerts solid the

solutions thermally

strain

be

aliovalent instance extrinsic mobility ionic it

The

reflect

should

seems

defects.

in

will

in m i n d

defect

from

data. that and

residual

like

densities,

calculations

likely

also w i t h

that

will

effects,

The

defect

of nH

impurities,

oxygen,

of

with x m mobilities. It

reduced

borne

the

vary

increase

conductivity

disparity

enhancement

term

enthalpy

composition.

~Hf in the p r e s e n t

generated

energy

migration

may

+ VCI,2

. VCI,I

+ B rci,2

CIBr,I

+ VBr,2

~ VBr,l

+ CiBr,2

need

not

for

due

and

this

with

ions

sites

for

one can e n v i s a g e

the

a-axis. ~

found

simplicity

This

would

solute

ions

be p r e s e n t

domains. (7)

It

that

domains which

differ

effects. cause

of

before

effects

isolated

and

on nHf

solute

well

anomalous

as

PbCIBr-type

of p a i r s

very

as

with

and m o r e

suggested

produce

may

the

along

the s o l u t e

more

fields

from

This

ions

be c o n c o r d a n t

content

has been

m a y well

ion

a continuous

in o r d e r e d

strain

ions

i, and

Therefore,

increasing

and also

in w h i c h

> ~ (// b - a x i s )

experimentally.

will

the

Cl--Br-

for Br-

(// a-axis)

for

of Figure

ignoring

pathway

content.

2, and CI-

exchange,

with

that will

PbCIBr

sites

inspection

conduction

imply

solute

co~Pound

site

pathways

illustrated

occupy

i. By

ion

be

the

dependence

of

AHf o n x in the r e g i o n ~ 0.3 A

< x < ~ 0.7.

detailed

details for

size

be

equimolecular Br-

may

increasing

can

extrinsic

local

account. preferential

conduction

and h e n c e

to

into the

occupancy,

this

the

taken

with

preferential

influence

In addition,

be

Together

pairs,

a minor

represented

x Brcl,l

This

the d e f e c t

assume

and h e n c e

defect

~

end m e m b e r s

the e x t r i n s i c

mobilities

thermal

that

the pure

equal.

minimum

~ ( P b B r 2)

jumps

by

develop

(PbCIBr) >

distortions

vacancy

from

region

lattice

or

end m e m b e r s

~ i0

about

intrinsic

as

densities,

mobilities

account.

temperature In

defect

defect

mobility

defect

enthalpy

increasing

whether

the

303

(tBr) Such

quantitative

anomalous of the

chloride as

a

Figure

transference (tc1), function are

6).

explanation

behaviour

experiments

undertaken.

(viz.

has

of

to await

number

data

and b r o m i d e

ions

of c o m p o s i t i o n . currently

being

304

M. Lumbreras et al./Mixed lead halides PbC12xBr 2( 1 -x). H 6).

ACKNOWLEDGEMENTS

The C.

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